Thomas M. Idzorek Chief Investment Officer Ibbotson Associates, A Morningstar Company Email: tidzorek@ibbotson.com James X. Xiong Senior Research Consultant Ibbotson Associates, A Morningstar Company Email: xiong@ibbotson.com Roger G. Ibbotson Chairman & CIO Zebra Capital Management, LLC Professor in Practice Yale School of Management Email: roger.ibbotson@yale.edu Ocber 1, 2010 The authors thank Eric Hu for building the program that allowed this research take place and Alexa Auerbach and Maciej Kowara at Morningstar for helpful comments. 1
Abstract Recent literature indicates that a liquidity investment style the process of investing in relatively less liquid scks within the liquid universe of publicly traded scks has led excess returns relative size, value, and momentum. We examine whether this style can be uncovered not just at the sck level, but at the mutual fund level. In aggregate and across a wide range of mutual fund categories, we find that on average mutual funds that hold less liquid scks significantly outperformed mutual funds that hold more liquid scks. This demonstrates that the liquidity premium is sufficiently strong show up in portfolios where the managers are not directly focusing on liquidity. Surprisingly, the outperformance of the mutual funds that hold less liquid scks was primarily due superior performance in down markets. 2
1. Introduction It is relatively well known that less liquid investments tend outperform more liquid investments. The same holds true within the relatively liquid universe of publicly traded scks. The generally accepted rationale for a liquidity premium is that all else equal, invesrs prefer greater liquidity; thus, in order induce invesrs hold less liquid assets, they must have the expectation (but not the guarantee) of a return premium. Using day s nomenclature, one could think of less liquidity as a risk facr, an exotic beta, or a structural alpha. Recent literature indicates that the liquidity investment style the process of investing in relatively less liquid scks within the liquid universe of publicly traded scks produced risk-adjusted returns that rival or exceed those of the three best-known market anomalies: value minus growth, small minus large, and momentum. For example, Amihud and Mendelson (1986) use the quoted bid-ask spread as a measure of liquidity and tested the relationship between sck returns and liquidity during the period of 1961-1980. They found evidence consistent with the notion of a liquidity premium. Datar, Naik, and Radcliffe (1998) use the turnover rate (number of shares traded as a fraction of the number of shares outstanding) as a proxy for liquidity and find that sck returns are strongly negatively related their turnover rates, confirming the notion that less liquid scks provide higher average returns. Overall, the results support the relationship between less liquidity and higher sck returns. Pásr and Stambaugh (2003) demonstrate that market-wide liquidity appears be a state variable that is important for pricing common scks. They find that expected sck returns are related crosssectionally the sensitivities of sck returns innovations in aggregate liquidity. 3
According their measure, smaller scks are less liquid and thus have high sensitivities aggregate liquidity. More recently, using monthly data for the largest 3,500 U.S. scks by capitalization, starting in 1972, Chen, Ibbotson, and Hu (2010) sort scks in equallyweighted quartiles based on liquidity. The results clearly show that annually-rebalanced composites of relatively less liquid scks significantly outperform composites of more liquid scks after controlling for size, valuation, and momentum. 1 They characterize liquidity as the missing style. Might this emerging investment style and risk facr be present and economically significant among mutual funds? If so, selecting mutual funds that are knowingly or unknowingly systematically constructing portfolios of less liquid scks suggests a strategy for not only creating mutual funds, but for selecting mutual funds that are more likely outperform their peers. 2. Data and Methodology To investigate whether mutual funds that hold less liquid scks tend outperform those that hold more liquid scks is a data intensive exercise. First, we need an individual sck database that enables us estimate the liquidity of each individual sck. Next, we need know the holdings of each individual mutual fund throughout time. Combining data from Morningstar s individual sck database with Morningstar s mutual fund holding database, we are able build composites of mutual funds based on the weighted average liquidity of the individual scks held by the mutual funds. 1 The results of Chen, Ibbotson, and Hu (2010) as well as earlier versions, are so compelling that results are documented and updated each year in Ibbotson s Scks, Bonds, Bills and Inflation Annual Year Book. 4
We begin with Morningstar s open-end equity mutual fund universe containing both alive and dead funds. Our primary focus is on the U.S. equity mutual funds, but we also include a sample of non-u.s. equity mutual funds. The Morningstar categories include those of the nine size-valuation style boxes that form the U.S. equity universe, the three valuation-based columns from the style box (value, core, and growth), and the three size-based rows from the style box (large, mid, and small), plus the non-u.s. category. Morningstar has either monthly or quarterly mutual fund holdings data starting in 1983. However, wide-scale holdings data for most funds was not available until 1995 for the U.S. equity fund universe (and starting in January 2000 for the non-u.s. equity fund universe). For the U.S. equity fund universe, holdings data from January 1995 is used form the starting composites that we begin tracking in February 1995. The constituents of the composites are based on the previous month s holdings information. This gives us 14 years and 11 months of U.S. performance hisry, and 9 years and 11 months of non- U.S. performance hisry. Table 1 summarizes the number of alive funds in the various universes/categories with the required data at the start of the study (Feb. 1995 for U.S. equity categories and Feb. 2000 for the non-u.s. equity fund universe) and at the end of the study. 5
Table 1: Number with Required Data Morningstar Category Start Date Number of Funds (Feb 1995) End Date Number of Funds (Dec 2009) Small Value 42 238 Small Core 73 369 Small Growth 123 494 Mid Value 45 229 Mid Core 84 314 Mid Growth 131 527 Large Value 212 719 Large Core 322 1260 Large Growth 262 1048 Small 238 1101 Mid 260 1070 Large 796 3027 Value 299 1186 Core 479 1943 Growth 516 2069 All U.S. 1294 5198 All Non-U.S.* 634 815 *Non-U.S. mutual funds data starts in February 2000. There are a number of potential measures of liquidity for an individual sck. For simplicity and consistency we used the basic sck level turnover measure used in Chen, Ibbotson and Hu: average daily shares traded over the last year divided by the number of shares outstanding. No attempt was made adjust the number of shares outstanding for free-float. Bringing the two databases gether enables us estimate each mutual fund s weighted-average liquidity at each point in time. For a given mutual fund, if we did not have a liquidity turnover ratio for a holding, we ignore the position and rescale the other holdings prior calculating the mutual fund s weighted average liquidity. 2 We study 2 In the case in which we lacked liquidity turnover ratios for more than 40% of the holdings, we ignored the fund completely. For U.S. equity funds, we had sck level liquidity turnover ratios for the vast majority of funds. For non-u.s. equity funds, only about 10% of funds had 60% or more sck level liquidity turnover ratios. 6
performance in two different ways: monthly-rebalanced composites and annuallyrebalanced composites. Monthly-Rebalanced Composites Armed with each mutual fund s weighted average sck level liquidity within any given category, we rank order the mutual funds based on their weighted average liquidity and use this information form monthly-rebalanced, equally-weighted composites (in our case, quintiles) of mutual funds with similar weighted average sck level liquidity scores. 3 Funds with the lowest weighted average liquidity are assigned the L1 quintile and funds with the highest weighted average liquidity are assigned the L5 quintile. The constituent mutual funds in the composite evolve each month, as the weighted average sck level liquidity of the mutual funds evolves. Following this type of strategy requires the invesr rebalance their portfolio of mutual funds monthly. Annually-Rebalanced Composites Next, we looked at the performance of annually-rebalanced mutual fund composites in which the quintiles are based on the mutual funds weighted average liquidity score over the previous year. More specifically, we break our nearly 15 year analysis period in 15 one-year segments. Additionally, we try determine if funds in the lowest liquidity composite (L1) are more likely outperform the funds in the highest liquidity composite (L5) for a holding period of one year. 3 We calculated the tal assets under management (AUM) of the composites looking for systematic patterns, somewhat expecting that the L1 (low liquidity) composite may systematically favor smaller mutual funds that can more readily invest in less liquid scks without a significant market impact. In contrast what we expected see, on average the L1 composite AUM was greater than that of the L5 composite: L1 = $929.87, L2 = $990.92, L3 = $984.73, L4 = $779.65, and L5 = $510.54. The numbers are in million dollars, and are averaged across the composite and over the entire periods. 7
3. Results 3.1 Monthly-Rebalanced, Equally-Weighted Composites For our monthly-rebalanced, equally-weighted composites, Table 2 summarizes the striking results for our entire universe and the 15 categories within our primary universe of U.S. equity funds. The table displays the annual arithmetic return, annual geometric return, standard deviation, Sharpe ratio, as well as the monthly alpha from a monthly return regression of the composite relative its category-average composite, with a t-statistic of the alpha. For each category, we show the difference in performance statistics from the lowest liquidity composite (L1) and the highest liquidity composite (L5). For each of the 16 groupings, the lowest liquidity composite (L1) had a superior annual arithmetic return, annual geometric return, standard deviation, Sharpe ratio, and monthly alpha when compared the applicable equally-weighted composite for that category. With the exception of the Growth category, the t-statistic of the alpha of the lowest liquidity composite exceeded 2.0, indicating that the alpha was statistically significant at the 95% confidence level. Furthermore, for the vast majority of groupings across the five quintiles, the results are mononic. We highlight the performance of the All composites at the botm of Table 2, representing our entire universe of U.S. equity funds. Comparing All L1 All L5, the annual geometric return was 2.65% higher, the standard deviation was much lower (24.83% vs. 15.25%), while the Sharpe ratio was nearly twice as high (.43 vs..23). The average geometric mean for the funds in the small cap category is higher than those in the large cap category over the 15-year period. The largest monthly alpha differences between the L1 (lowest liquidity) and L5 (highest liquidity) quintiles occurred 8
within the Small and Mid categories (both were 59 basis points), while the smallest monthly alpha difference occurred for the Large Core category (23 basis points). These results, as well as the rest of the results reported in Table 2, are consistent with the sck level results in Chen, Ibbotson and Hu (2010), despite the difference in sample period. 9
Table 2: Monthly-Rebalanced Composites Performance Statistics U.S. Equity Fund Universe (Feb. 1995 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity 10 Standard Deviation Monthly Alpha T- Statistic of Alpha N Periods Arithmetic Mean Geometric Mean Sharpe Ratio Small Value L1 179 12.26 10.86 17.61 0.50 0.14 2.69 Small Value L2 179 12.50 10.79 19.55 0.46 0.06 1.46 Small Value L3 179 11.91 10.17 19.63 0.43 0.01 0.26 Small Value L4 179 11.26 9.48 19.81 0.39-0.05-1.17 Small Value L5 179 10.05 8.09 20.75 0.31-0.18-2.20 Small Value 179 11.59 9.91 19.27 0.42 -- -- L1 - L5 2.21 2.77-3.15 0.18 0.32 -- Small Core L1 179 12.67 11.25 17.74 0.51 0.24 3.21 Small Core L2 179 11.14 9.48 19.09 0.40 0.05 0.88 Small Core L3 179 10.71 8.81 20.43 0.35-0.05-1.35 Small Core L4 179 10.93 8.73 22.07 0.34-0.10-1.76 Small Core L5 179 10.13 7.94 21.98 0.30-0.16-2.09 Small Core 179 11.11 9.29 20.02 0.38 -- -- L1 - L5 2.54 3.32-4.24 0.21 0.40 -- Small Growth L1 179 11.15 9.26 20.44 0.37 0.23 2.15 Small Growth L2 179 10.43 7.88 23.91 0.29 0.04 0.81 Small Growth L3 179 9.87 6.87 25.93 0.24-0.08-1.77 Small Growth L4 179 11.50 8.13 27.84 0.29 0.00 0.01 Small Growth L5 179 10.04 6.26 29.30 0.22-0.17-2.58 Small Growth 179 10.60 7.77 25.22 0.28 -- -- L1 - L5 1.10 3.00-8.86 0.15 0.40 -- Mid Value L1 179 12.15 11.06 15.52 0.56 0.19 3.66 Mid Value L2 179 11.28 9.95 17.13 0.45 0.04 0.69 Mid Value L3 179 11.11 9.76 17.23 0.44 0.02 0.35 Mid Value L4 179 11.45 9.82 18.92 0.42-0.04-0.75 Mid Value L5 179 9.72 7.81 20.39 0.30-0.24-2.52 Mid Value 179 11.14 9.73 17.56 0.43 -- -- L1 - L5 2.42 3.25-4.87 0.25 0.43 -- Mid Core L1 179 11.81 10.66 15.87 0.52 0.22 2.32 Mid Core L2 179 11.58 10.06 18.29 0.44 0.07 1.13 Mid Core L3 179 12.02 10.24 19.86 0.43 0.03 0.54 Mid Core L4 179 11.12 9.22 20.49 0.37-0.08-1.38 Mid Core L5 179 9.65 7.47 21.86 0.28-0.24-2.24 Mid Core 179 11.23 9.61 18.87 0.41 -- -- L1 - L5 2.16 3.19-5.99 0.24 0.46 -- Mid Growth L1 179 11.27 9.82 17.94 0.43 0.28 2.36 Mid Growth L2 179 11.26 9.14 21.82 0.35 0.11 1.87 Mid Growth L3 179 11.01 8.38 24.38 0.31-0.01-0.30 Mid Growth L4 179 10.39 7.35 26.15 0.26-0.12-2.32 Mid Growth L5 179 10.19 6.63 28.46 0.23-0.21-2.40 Mid Growth 179 10.82 8.38 23.39 0.31 -- -- L1 - L5 1.08 3.18-10.52 0.20 0.49 -- Large Value L1 179 9.41 8.44 14.49 0.41 0.13 3.67 Large Value L2 179 8.75 7.65 15.38 0.34 0.04 1.59 Large Value L3 179 8.61 7.42 16.04 0.32 0.00-0.15 Large Value L4 179 8.34 7.07 16.53 0.29-0.05-2.29 Large Value L5 179 7.52 6.11 17.32 0.23-0.14-2.98 Large Value 179 8.52 7.35 15.88 0.31 -- -- L1 - L5 1.89 2.33-2.83 0.18 0.28 -- Large Core L1 179 8.95 7.95 14.69 0.37 0.14 2.88 Large Core L2 179 8.10 6.91 15.98 0.29 0.01 0.70 Large Core L3 179 7.97 6.66 16.76 0.27-0.03-1.21 Large Core L4 179 7.63 6.35 16.56 0.25-0.05-2.66 Large Core L5 179 7.84 6.30 18.12 0.24-0.08-1.39 Large Core 179 8.10 6.86 16.31 0.28 -- -- L1 - L5 1.11 1.65-3.42 0.13 0.23 --
Table 2: Monthly-Rebalanced Composites Performance Statistics continued U.S. Equity Fund Universe (Feb. 1995 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity 11 Standard Deviation Monthly Alpha T- Statistic of Alpha N Periods Arithmetic Mean Geometric Mean Sharpe Ratio Large Growth L1 179 8.80 7.61 16.04 0.33 0.16 2.01 Large Growth L2 179 8.36 6.92 17.64 0.27 0.06 1.24 Large Growth L3 179 7.48 5.86 18.62 0.21-0.05-2.01 Large Growth L4 179 8.63 6.74 20.30 0.25-0.01-0.44 Large Growth L5 179 8.60 5.87 24.52 0.21-0.14-1.38 Large Growth 179 8.38 6.68 19.15 0.25 -- -- L1 - L5 0.20 1.75-8.48 0.12 0.31 -- Small L1 179 12.61 11.12 18.19 0.50 0.34 2.45 Small L2 179 11.19 9.36 20.06 0.38 0.12 1.25 Small L3 179 10.72 8.40 22.74 0.32-0.04-1.42 Small L4 179 10.59 7.76 25.28 0.28-0.14-1.68 Small L5 179 9.91 6.75 26.62 0.24-0.25-2.48 Small 179 11.00 8.82 22.01 0.34 -- -- L1 - L5 2.70 4.37-8.42 0.26 0.59 -- Mid L1 179 11.42 10.24 16.08 0.49 0.32 2.13 Mid L2 179 11.58 10.00 18.70 0.43 0.17 1.91 Mid L3 179 11.28 9.25 21.29 0.36 0.02 0.54 Mid L4 179 10.34 7.75 24.07 0.28-0.17-2.63 Mid L5 179 10.08 6.91 26.70 0.25-0.27-2.24 Mid 179 10.94 9.01 20.69 0.36 -- -- L1 - L5 1.34 3.33-10.62 0.25 0.59 -- Large L1 179 9.35 8.34 14.81 0.39 0.20 2.10 Large L2 179 8.66 7.49 15.92 0.32 0.08 1.46 Large L3 179 7.71 6.41 16.72 0.25-0.04-1.29 Large L4 179 7.44 6.01 17.46 0.22-0.09-2.84 Large L5 179 8.11 6.03 21.23 0.22-0.15-1.21 Large 179 8.25 6.93 16.83 0.28 -- -- L1 - L5 1.24 2.30-6.42 0.18 0.35 -- Growth L1 179 9.38 8.10 16.67 0.35 0.20 1.72 Growth L2 179 8.78 7.18 18.61 0.28 0.05 0.80 Growth L3 179 9.36 7.34 21.02 0.28 0.01 0.30 Growth L4 179 10.50 7.83 24.46 0.28-0.01-0.18 Growth L5 179 9.18 5.85 27.34 0.21-0.21-1.88 Growth 179 9.44 7.40 21.17 0.28 -- -- L1 - L5 0.20 2.26-10.67 0.14 0.40 -- Core L1 179 10.15 9.12 15.04 0.44 0.18 2.86 Core L2 179 9.10 7.84 16.54 0.34 0.02 0.42 Core L3 179 8.57 7.21 17.09 0.29-0.05-1.28 Core L4 179 8.90 7.43 17.81 0.30-0.05-1.44 Core L5 179 9.39 7.48 20.37 0.29-0.10-0.89 Core 179 9.22 7.87 17.08 0.33 -- -- L1 - L5 0.76 1.63-5.33 0.15 0.27 -- Value L1 179 10.30 9.29 14.86 0.46 0.15 3.28 Value L2 179 9.56 8.40 15.87 0.38 0.03 1.09 Value L3 179 9.55 8.27 16.68 0.36 0.00-0.22 Value L4 179 9.26 7.92 17.03 0.34-0.05-1.91 Value L5 179 8.59 7.01 18.39 0.27-0.15-1.96 Value 179 9.45 8.20 16.43 0.36 -- -- L1 - L5 1.71 2.28-3.53 0.18 0.29 -- All L1 179 10.16 9.09 15.25 0.43 0.23 2.05 All L2 179 9.24 7.98 16.56 0.35 0.08 1.06 All L3 179 8.58 7.15 17.58 0.29-0.03-0.75 All L4 179 9.44 7.58 20.16 0.29-0.07-1.19 All L5 179 9.22 6.44 24.83 0.23-0.22-1.33 All 179 9.33 7.80 18.20 0.32 -- -- L1 - L5 0.94 2.65-9.58 0.21 0.45 --
Observing the 15-year hisry for the five All liquidity quintiles reveals an interesting result (see Figure 1). For the most part, the lower liquidity composites dominate; however, for a brief period corresponding with the height of the technology bubble, the higher liquidity composites (blue and green lines in Figure 1) temporarily dominated. During this irrational period, invesrs could not get enough of the most liquid scks benefiting the mutual funds holding these glamour scks. Interestingly, the brief outperformance of high-liquidity composites during the technology bubble is not as prevalent or nonexistent in the value-oriented categories, as illustrated in Figure 2, showing the growth of a dollar among the mutual fund composites constructed from the value-oriented fund categories. We suspect this noteworthy pattern is less prevalent among value managers, as they were unlikely hold technology scks at that time. 12
Figure 1: Growth of $1 All Liquidity Composites (Feb. 1995 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity $10 All L1 All L2 All L3 All L4 All L5 All $1 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Figure 2: Growth of $1 Value Liquidity Composites (Feb. 1995 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity $10 L1 L2 L3 L4 L5 $1 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 13
Table 3 reports various up-side and down-side return capture statistics for our All composites. The superior overall performance of the low liquidity quintile(s) has primarily come from superior performance in down markets. Table 3: Monthly Up-side / Down-side Capture Statistics U.S Equity Fund Universe (Feb. 1995 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity Up Periods Down Periods Up Return Down Return Up Market Return Down Market Return Up- Market Capture Down- Market Capture Decline Number of Drawdowns All L1 117 62 3.04-3.39 3.03-3.09 86.31 75.93 91.04 28 All L2 112 67 3.37-3.67 3.30-3.75 93.91 91.88 97.57 21 All L3 109 70 3.65-3.93 3.47-4.19 98.73 102.57 97.28 18 All L4 107 72 4.20-4.36 3.89-4.75 110.45 116.32 89.07 18 All L5 106 73 4.90-5.30 4.37-5.63 123.01 138.71 75.34 10 All 109 70 3.80-4.02 3.61-4.28 102.78 104.85 95.11 18 Monthly Up-side / Down-side Capture statistics are from Morningstar EnCorr. Up Periods and Down Periods simply report the tal number of up and down monthly returns in the sample of 179 months. The Up Return and Down Return statistics report the average of all positive returns and all negative returns in the sample, respectively. The Up Market Return and Down Market Return report similar statistics based on the performance of the market, which in this case is defined as the Russell 3000. The Up-Market Capture and Down- Market Capture identify the percentage of the market s up and down movements that are captured, respectively, where numbers greater than 100 indicate more sensitivity than the Russell 3000. The Decline identifies the average peak trough loss. The Number of Drawdowns identifies the number of peak trough occurrences. Many people find the results in Table 3 puzzling as their intuition tells them that in down markets, less liquid scks (and the funds that hold them) should suffer the steepest declines. We posit that one cause of the superior downside performance of the low liquidity quintile relates the type of strategies typically used by low liquidity (L1) managers versus high liquidity (L5) managers. We suspect that, on average, the funds that find themselves in L1 have less turnover than those in L5, reflecting a general preference for a longer holding period strategy. In contrast, L5 managers likely have higher turnover and, on average, use strategies that involve more frequent trading. Funds that trade frequently pay greater attention trading costs and are more likely use 14
liquidity-based measures, such as bid-ask spreads, screen out relatively less liquid scks. Furthermore, during periods of turmoil, L5 managers may be more likely trade; thus, the most liquid scks may, in fact, suffer the steepest declines because there is a greater propensity for their owners trade them. We can examine a mutual fund s standard turnover statistic. Standard turnover is a measure of how much a mutual fund turns over its portfolio and should not be confused with our liquidity turnover measure, which measures the average liquidity of the individual sck holdings. We confirm that the average standard turnover ratio of L5 mutual funds was significantly higher than the average standard turnover ratio of L1 mutual funds by calculating the average standard turnover of each quintile at each point in time and then taking the average through time. The average annual turnover across the composite and over time for L1 was 59% for the mutual funds with the less liquid scks and 124% for the L5 mutual funds with the most liquid scks for the entire U.S. mutual fund universe. Switching back the our liquidity measure, the average liquidity measure for the five quintiles for U.S. equity funds over the almost 15 years are shown in Table 4. Once again, the liquidity of a holding sck is measured as its average daily shares traded over the last year divided by the number of shares outstanding. The liquidity of a fund is then calculated as the weighted average liquidity of the scks it holds. The small growth category had the largest liquidity difference between composite L5 and L1, 3.73% (=4.38% - 0.65%), while the large value category had the smallest liquidity difference, 0.51% (=0.88%-0.37%). 4 Multiplying the daily figures by 250 (representing the approximate number of trading days per year) produces annualized figures that some 4 Somewhat curiously, even though the scks in the large value category seemed have the smallest liquidity difference, in Table 2, the alpha of the L1 composite for the large value category had the highest t- statistic. 15
might find more intuitive. For example, multiplying the small growth daily figures by 250 leads 932% (=1095% - 163%), indicating that, on average, every outstanding share of sck trades 10.95 times per year for the L5 composite and 1.63 times per year for the L1 small growth composite. In general, small funds and growth funds have larger liquidity differences than large funds and value funds, respectively, indicating that small categories and growth categories tend hold relatively heavily traded scks. The liquidity measure for the All U.S. sample with the LI (lowest liquidity) mutual funds contained scks that had average turnover of 110% per year. All but two categories in Table 4 (large value and value) had average sckholdings with annual turnover rates exceeding 100% per year. Table 4: The Sck Level Liquidity Measure U.S Equity Fund Universe (Feb. 1995 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity Daily Annualized Category L1 L2 L3 L4 L5 L1 L2 L3 L4 L5 Small Value 0.43% 0.57% 0.67% 0.83% 2.18% 108% 143% 168% 208% 545% Small Core 0.47% 0.65% 0.80% 1.05% 3.17% 118% 163% 200% 263% 793% Small Growth 0.65% 0.91% 1.16% 1.52% 4.38% 163% 228% 290% 380% 1095% Mid Value 0.44% 0.55% 0.65% 0.81% 1.97% 110% 138% 163% 203% 493% Mid Core 0.47% 0.66% 0.83% 1.04% 2.44% 118% 165% 208% 260% 610% Mid Growth 0.63% 0.87% 1.09% 1.42% 3.23% 158% 218% 273% 355% 808% Large Value 0.37% 0.45% 0.52% 0.60% 0.88% 93% 113% 130% 150% 220% Large Core 0.42% 0.54% 0.60% 0.67% 1.08% 105% 135% 150% 168% 270% Large Growth 0.51% 0.64% 0.75% 0.92% 1.80% 128% 160% 188% 230% 450% Small 0.50% 0.72% 0.93% 1.26% 3.71% 125% 180% 233% 315% 928% Mid 0.51% 0.73% 0.93% 1.23% 2.91% 128% 183% 233% 308% 728% Large 0.42% 0.54% 0.62% 0.74% 1.37% 105% 135% 155% 185% 343% Value 0.38% 0.48% 0.55% 0.65% 1.31% 95% 120% 138% 163% 328% Core 0.44% 0.56% 0.64% 0.78% 1.82% 110% 140% 160% 195% 455% Growth 0.54% 0.71% 0.89% 1.18% 2.90% 135% 178% 223% 295% 725% All US 0.44% 0.58% 0.70% 0.92% 2.29% 110% 145% 175% 230% 573% To test the robustness of the results reported in Table 2 an implementation delay due the availability of timely holdings data, we repeated the analysis under the 16
assumption of a one-quarter implementation delay. The results were quantitatively and qualitatively similar Table 2. Due space considerations, we only present the results for our entire U.S. equity universe All composites (see Table 5). The quarterly implementation lag decreased our data points 176 from 179, but the key statistics in Table 5 are very similar the statistics for the corresponding All composite listed at the botm of Table 2. If anything, the implementation lag slightly enhanced performance. Notice that with no implementation delay (botm of Table 2), the Geometric Mean return for the All L1 composite exceed that of the All L5 composite by 2.65%. With the 3-month implementation delay (Table 5) the difference surprisingly increased 3.26%. Table 5: Monthly-Rebalanced Composites with Quarterly Implementation Delay Performance Statistics U.S. Equity Fund Universe (April 1995 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity Standard Deviation Monthly Alpha T- Statistic of Alpha N Periods Arithmetic Mean Geometric Mean Sharpe Ratio All L1 176 9.89 8.83 15.17 0.42 0.25 2.19 All L2 176 9.00 7.74 16.48 0.33 0.10 1.29 All L3 176 8.14 6.68 17.70 0.26-0.03-0.61 All L4 176 8.66 6.76 20.28 0.25-0.08-1.59 All L5 176 8.34 5.58 24.69 0.20-0.23-1.48 All 176 8.80 7.26 18.24 0.29 -- -- L1 - L5 1.55 3.26-9.52 0.23 0.48 -- Going beyond the universe of U.S. equity funds, we repeated our analysis (without the implementation delay) using a universe of non-u.s. equity funds (see Table 6). Unfortunately, our sample size was much smaller, as we lacked the required individual sck data and / or the holdings data for a relatively large number of funds. Therefore, this small sample may not represent non-u.s. equity funds well. Due the lack of data availability, our start date was moved from Feb. 1995 Feb. 2000, and we 17
did not break the universe in sub-categories. Overall, this nearly 10-year period was not particularly good for scks. The results are less compelling than those of the U.S. mutual fund universe. The Non-US All L2 quartile has the highest Sharpe ratio. The Geometric Mean return of L1 continued trump that of L5, but in this case it was mostly due the dismal return of L5 rather than standout performance of L1. None of the monthly alphas were significant. Table 6: Monthly-Rebalanced Composites Performance Non-U.S. Equity Fund Universe (Feb. 2000 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity Standard Deviation Monthly Alpha T- Statistic of Alpha N Periods Arithmetic Mean Geometric Mean Sharpe Ratio All L1 119 3.28 1.50 19.16 0.03 0.04 0.40 All L2 119 4.07 2.69 16.90 0.08 0.14 1.28 All L3 119 2.97 1.58 16.92 0.01 0.05 0.37 All L4 119 2.37 0.74 18.27-0.02-0.02-0.15 All L5 119 1.13-1.63 23.84-0.07-0.18-0.77 All 119 2.76 1.15 18.19 0.00 -- -- L1 - L5 2.15 3.13-4.69 0.10 0.22 -- 3.2 Annually-Rebalanced, Equally-Weighted Composites For all practical purposes, buying and selling numerous different mutual funds each month or each quarter in order hold the mutual funds with the least liquid sck holdings is impractical. Although one would expect it be a less pure way of gathering exposure low liquidity scks, would simply buying an annually-rebalanced basket of mutual funds each year with the lowest average weighted average liquidity measure in the previous year produce similar results? To test this, we calculated the performance of annually-rebalanced composites of mutual funds. Table 7 contains the results. 18
Table 7: Annually-Rebalanced Composites Performance Statistics U.S. Equity Fund Universe (Jan. 1996 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity 19 Standard Deviation Monthly Alpha T- Statistic of Alpha N Periods Arithmetic Mean Geometric Mean Sharpe Ratio Small Value L1 168 12.19 10.70 18.19 0.48 0.37 2.66 Small Value L2 168 10.33 8.43 20.52 0.34 0.11 1.17 Small Value L3 168 7.10 4.90 21.89 0.17-0.22-4.79 Small Value L4 168 11.41 8.56 25.60 0.31 0.02 0.20 Small Value L5 168 7.04 3.89 26.29 0.14-0.37-3.65 Small Value 168 9.59 7.42 21.92 0.28 -- -- L1 - L5 5.15 6.81-8.10 0.34 0.74 -- Small Core L1 168 10.98 9.52 17.92 0.42 0.13 1.78 Small Core L2 168 12.17 10.51 19.27 0.46 0.17 3.09 Small Core L3 168 11.20 9.28 20.58 0.38 0.03 0.66 Small Core L4 168 9.08 6.87 21.96 0.26-0.20-3.53 Small Core L5 168 9.58 7.40 21.95 0.28-0.15-1.98 Small Core 168 10.60 8.76 20.11 0.36 -- -- L1 - L5 1.40 2.12-4.02 0.14 0.29 -- Small Growth L1 168 10.43 8.48 20.76 0.34 0.21 2.18 Small Growth L2 168 8.48 5.92 23.76 0.21-0.06-1.49 Small Growth L3 168 10.99 8.09 25.69 0.30 0.10 1.66 Small Growth L4 168 9.64 6.33 27.40 0.23-0.07-1.09 Small Growth L5 168 8.26 4.72 28.16 0.17-0.20-3.29 Small Growth 168 9.56 6.78 24.93 0.25 -- -- L1 - L5 2.17 3.76-7.40 0.17 0.42 -- Mid Value L1 168 11.48 10.28 16.25 0.50 0.19 3.30 Mid Value L2 168 9.99 8.58 17.51 0.38 0.01 0.12 Mid Value L3 168 9.46 8.10 17.21 0.35-0.03-0.49 Mid Value L4 168 9.77 8.13 18.85 0.34-0.07-1.31 Mid Value L5 168 9.90 8.06 20.14 0.32-0.11-1.34 Mid Value 168 10.12 8.68 17.74 0.38 -- -- L1 - L5 1.58 2.22-3.88 0.17 0.30 -- Mid Core L1 168 10.65 9.44 16.28 0.45 0.18 2.04 Mid Core L2 168 10.42 8.89 18.24 0.39 0.06 1.14 Mid Core L3 168 10.48 8.63 20.13 0.35-0.01-0.31 Mid Core L4 168 10.34 8.50 20.10 0.35-0.02-0.48 Mid Core L5 168 8.72 6.55 21.73 0.25-0.21-1.99 Mid Core 168 10.12 8.47 18.97 0.35 -- -- L1 - L5 1.93 2.89-5.45 0.20 0.39 -- Mid Growth L1 168 10.27 8.69 18.61 0.37 0.25 2.37 Mid Growth L2 168 9.75 7.48 22.43 0.28 0.07 1.68 Mid Growth L3 168 9.21 6.55 24.32 0.24-0.04-0.91 Mid Growth L4 168 8.52 5.65 25.31 0.20-0.12-2.31 Mid Growth L5 168 8.49 5.27 26.85 0.19-0.17-2.34 Mid Growth 168 9.25 6.81 23.25 0.25 -- -- L1 - L5 1.78 3.42-8.24 0.18 0.42 -- Large Value L1 168 7.39 6.39 14.61 0.27 0.05 1.39 Large Value L2 168 7.60 6.49 15.44 0.27 0.03 1.42 Large Value L3 168 7.40 6.23 15.86 0.25 0.00-0.04 Large Value L4 168 7.03 5.76 16.44 0.22-0.05-2.60 Large Value L5 168 7.63 6.27 17.04 0.25-0.02-0.55 Large Value 168 7.41 6.24 15.81 0.25 -- -- L1 - L5-0.23 0.12-2.43 0.03 0.07 -- Large Core L1 168 7.32 6.28 14.86 0.26 0.09 2.14 Large Core L2 168 6.67 5.53 15.61 0.21 0.01 0.56 Large Core L3 168 6.74 5.45 16.59 0.20-0.02-0.74 Large Core L4 168 6.63 5.34 16.57 0.20-0.03-1.37 Large Core L5 168 6.56 5.09 17.66 0.18-0.06-1.21 Large Core 168 6.78 5.55 16.18 0.21 -- -- L1 - L5 0.76 1.19-2.80 0.08 0.16 --
Table 7: Annually-Rebalanced Composites Performance Statistics continued U.S. Equity Fund Universe (Jan. 1996 Dec. 2009) Mutual Fund Quintiles, where L1 = Lowest Liquidity and L5 = Highest Liquidity 20 Standard Deviation Monthly Alpha T- Statistic of Alpha N Periods Arithmetic Mean Geometric Mean Sharpe Ratio Large Growth L1 168 8.12 6.85 16.58 0.29 0.16 2.40 Large Growth L2 168 6.43 4.97 17.60 0.17-0.02-0.36 Large Growth L3 168 6.97 5.39 18.39 0.19 0.00 0.13 Large Growth L4 168 7.33 5.42 20.24 0.19-0.02-0.72 Large Growth L5 168 6.81 4.40 22.81 0.15-0.13-1.29 Large Growth 168 7.13 5.46 18.91 0.20 -- -- L1 - L5 1.31 2.44-6.23 0.14 0.29 -- Small L1 168 11.74 10.26 18.07 0.46 0.30 2.31 Small L2 168 11.46 9.60 20.30 0.40 0.17 1.82 Small L3 168 9.26 6.94 22.62 0.26-0.12-4.94 Small L4 168 10.80 8.03 25.06 0.30-0.07-0.80 Small L5 168 8.45 5.45 25.82 0.20-0.29-2.99 Small 168 10.33 8.17 21.89 0.32 -- -- L1 - L5 3.29 4.82-7.75 0.27 0.59 -- Mid L1 168 10.35 9.12 16.42 0.42 0.28 1.94 Mid L2 168 10.48 8.81 19.16 0.37 0.14 1.91 Mid L3 168 9.83 7.75 21.40 0.30 0.00-0.05 Mid L4 168 9.10 6.59 23.58 0.24-0.14-2.16 Mid L5 168 8.28 5.35 25.56 0.19-0.26-2.17 Mid 168 9.61 7.66 20.67 0.30 -- -- L1 - L5 2.07 3.77-9.13 0.23 0.54 -- Large L1 168 7.86 6.83 14.91 0.30 0.15 1.73 Large L2 168 7.27 6.11 15.73 0.25 0.06 1.30 Large L3 168 6.45 5.17 16.48 0.19-0.04-1.40 Large L4 168 6.72 5.31 17.34 0.19-0.04-1.47 Large L5 168 6.85 4.91 20.39 0.17-0.11-1.00 Large 168 7.03 5.73 16.66 0.22 -- -- L1 - L5 1.01 1.92-5.48 0.13 0.26 -- Growth L1 168 8.12 6.80 16.86 0.28 0.15 1.41 Growth L2 168 7.44 5.82 18.63 0.22 0.02 0.32 Growth L3 168 8.66 6.60 21.23 0.25 0.03 1.78 Growth L4 168 8.65 6.13 23.61 0.22-0.03-0.55 Growth L5 168 8.30 5.15 26.54 0.18-0.14-1.20 Growth 168 8.23 6.21 20.97 0.23 -- -- L1 - L5-0.18 1.65-9.68 0.10 0.29 -- Core L1 168 8.68 7.62 15.10 0.35 0.13 2.16 Core L2 168 7.87 6.65 16.20 0.28 0.02 0.29 Core L3 168 7.59 6.27 16.80 0.25-0.04-0.94 Core L4 168 8.16 6.61 18.21 0.26-0.04-1.15 Core L5 168 8.68 6.78 20.28 0.26-0.05-0.49 Core 168 8.20 6.84 17.04 0.28 -- -- L1 - L5 0.00 0.84-5.18 0.09 0.18 -- Value L1 168 8.35 7.34 14.79 0.34 0.05 1.19 Value L2 168 8.26 7.09 15.79 0.31 0.00 0.04 Value L3 168 8.84 7.56 16.62 0.33 0.01 0.56 Value L4 168 8.92 7.55 17.18 0.32 0.00-0.13 Value L5 168 8.61 7.06 18.30 0.28-0.06-0.74 Value 168 8.59 7.35 16.39 0.32 -- -- L1 - L5-0.26 0.27-3.52 0.05 0.11 -- All L1 168 8.92 7.86 15.17 0.36 0.20 1.84 All L2 168 7.86 6.61 16.33 0.27 0.05 0.64 All L3 168 7.83 6.39 17.57 0.25-0.01-0.18 All L4 168 8.42 6.53 20.28 0.25-0.06-1.07 All L5 168 8.42 5.81 24.03 0.21-0.15-0.97 All 168 8.29 6.77 18.09 0.27 -- -- L1 - L5 0.50 2.05-8.87 0.16 0.35 --
Like the monthly-rebalanced results reported earlier in Table 2, the annuallyrebalanced results in Table 7 are extremely positive. For each of the 16 groupings, the lowest liquidity composite (L1) had a superior annual arithmetic return, annual geometric return, standard deviation, Sharpe ratio, and monthly alpha when compared the applicable equally-weighted composite for that category. In many cases the annuallyrebalanced L1 composite outperformed the comparable monthly-rebalanced L1 composite. However, due the smaller samples, the L1 monthly alpha was only statistically significant for 9 of 16 groupings, versus 15 of 16 groupings for the monthlyrebalanced composites. 4. Conclusions This study applies the liquidity style mutual funds. We show that mutual funds that hold relatively less liquid scks from within the liquid universe of publicly-traded scks outperform mutual funds that hold relatively more liquid scks. The results were confirmed by the monthly-rebalanced mutual fund composites for our universe of U.S. equity mutual funds, as well as for the nine size-valuation style boxes, the three valuation-based columns from the style box (value, core, and growth), and the three size-based rows from the style box (large, mid, and small). More specifically, for each of the 16 groupings, the lowest liquidity composite (L1) had a superior annual arithmetic return, annual geometric return, standard deviation, Sharpe ratio, and monthly alpha when compared the applicable highest liquidity composite (L5). For all but the Growth category, the t-statistic of the alpha of the lowest liquidity composite was statistically significant. Rerunning the analysis with a one quarter implementation delay led similar overall results. When looking at annually-rebalanced 21
composites of mutual funds based on the mutual funds weighted average liquidity score over the previous year, we found very similar results, with only a minor drop-off in overall performance. Taken gether, the results based on a one quarter implementation delay and the results based on annual rebalancing, the less liquid investment style or signal, seems last relatively long. Surprisingly, the outperformance of the mutual funds that hold less-liquid scks was primarily due superior performance in down markets. Finally, the results are less compelling for non-u.s. equity funds than those of the U.S. mutual fund universe, although this result is less conclusive given the lack of available data. Overall, the liquidity investment style is clearly present in mutual funds and leads dramatic differences in performance. 22
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